Ch:4 - Learning In The CollectiveQuote: "This core aspect of education in the new culture of learning presents a model for understanding learning in the face of rapid change. Teachers no longer need to scramble to provide the latest up-to-date information to students because the students themselves are taking an active role in helping to create and mold it, particularly in areas of social information."

Question: This chapter focuses on the idea of collectives as an avenue for learning and gives examples of how groups can come together to expand their knowledge. My question is can collectives be leveraged to bring about structured learning? How would you structure a question or problem such that a collective would be the best method for solving it?

Connection: I have made heavy use of the collectives available on stackexchange throughout my 20% project and my degree. This site has specific subgroups of professionals that have provided years worth of answers to questions and have been able to direct me to solutions when I have asked for assistance. I understand the power of collaborative groups like this, however I am highly inquisitive and self study regularly. I'm not sure how I could translate the use and worth of these types of sites to students who are truly disengaged with math.

Epiphany/Aha: The last paragraph of the chapter actually answers my initial question. These collectives are powerful tools that students should know about and be familiar with, however trying to focus them and direct them towards traditional models of education will be ineffective. These types of learning environments will always be too fluid to allow for traditional learning objectives and goals.

Ch:5 - The Personal With The CollectiveQuote: "The learning that happens through blogs, social networks, and other new media may be deeply grounded in experience and personal expression, but it also arises from the contributions of multiple people and voices. Expertise and authority are dispersed rather than centralized, and once a digital space hits a point of critical mass, it is very likely that some member of the community will have valuable expertise to share about a given topic."

Question: This chapter deals with blogs as a collective for pooling knowledge and skill to find solutions to problems. My question is how should you go about cultivating this pool of knowledge? While the search for interesting authors can be enlightening, it can also lead to dead ends and bad information. Without a central location to refer to it becomes difficult to find the great blogs hidden away and most people will end up concentrated around the major talking heads of any community.

Connection: I have personally found some great posts about math education while searching for help with writing a lesson plan. The problem is that many of these posts are on blogs that haven't been updated in years. I feel that some of these teachers might have started out with grand ideas and some really interesting lessons and then found that the community for their ideas was too spread out and quit blogging before it had a chance to connect with anyone.

Epiphany/Aha: I feel that the important take away from this chapter is the idea that we can introduce students to learning that they perceive of as fun. I have seen students work on problems that weren't assigned to them because the problems had the right ratio of difficulty to skill. I feel that students will work harder to solve a problem if they feel it is difficult but solvable than they will for a problem that is easy to solve. Striving for something that is just out of reach is much more rewarding. Creating learning environments with the tools of the new information age requires that we think of ways to implement lessons that have these qualities.

Ch:6 - We Know More Than We Can SayQuote: "Yet finding answers and memorizing facts do little to inspire students' passion to learn. If anything, they dull that desire and make learning a tiresome burden."

Question: How do we best go about finding and designing lessons that focus on inquiry based learning? We need questions that the students respond to and want to answer, not simply the questions we as teachers consider important. How do you direct students towards learning objectives in this systems?

Connection: We focused on the idea of inquiry based learning in our mathematical methods class. The idea that students can learn and retain knowledge when they discover it through a more organic process than simply answering stock questions was a key tenet of the class.

Epiphany/Aha: This chapter also touches on the idea of learning as play. I feel that this will probably be the major direction and advancement in education in the coming years as I feel that it will provide the best results for students learning and engagement. The traditional model is too boring for most students today let alone students of the past. To hold to that model will never bring the engagement that students require now.